On Monday, a state arbitrator ruled that Dewey HS’ ex-principal should be reinstated with back pay despite charges of egregious abuse of credit-recovery and other suspect academic practices that allowed students to graduate without course mastery.

How could the city’s Department of Education let this happen? Because, the arbitrator found, the DOE approved all student grades coming out of this scam.

It is beyond time to raise the roof over shortchanging kids to make supposed educators look good. Like big banks that set their own rules, skirting ethical boundaries, educrats in Albany and the DOE promote failure without consequence.

Last June’s DOE Office of Special Investigations Report on the Dewey cheating scandal documented innumerable instances where the principal and her cronies engineered undeserved credits to meet DOE-dictated benchmarks.

“There is no dispute that students were not required to receive instruction to obtain credit,” the report found. In addition, conditions set for Dewey’s “PM School,” held after school, and “Project Graduation” credit-bearing courses made “appropriate academic instruction impossible.”

Yet, despite its own investigators’ findings, DOE honchos approved credits gained through this scam, leading to this week’s exoneration of the Dewey principal.

In February, a high-level DOE task force found that 36 schools mismanaged online classes and credit-recovery programs, yet no disciplinary actions were taken.

State education regulations are so lax that it’s easy to avoid even these findings by finessing assignments and assessments, especially online, to avoid course failure or allow subsequent “recovery.” Principals can code students’ transcripts so that fraud is undetected unless already suspected.

The task-force report was accompanied by a DOE promise “to be proactive.”

It is easy to blame the unrealistic no-excuses system of school accountability for this disregard of true merit. But teachers at Dewey were the ones who blew the whistle on the charade that, in theory, undercut their own record of “success.”

The higher-ups are the ones who need a spine, tightening regulations and oversight to discourage and eliminate this wanton academic chicanery.

David C. Bloomfield is a professor of education leadership, law and policy at Brooklyn College and the CUNY Graduate Center. His American Public Education Law, 3rd Ed., will be published this summer.